1. In class, we talked about the transformation-based definition of similarity:
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Question
1. In class, we talked about the transformation-based definition of similarity: that two plane figures F and G are similar if there is a sequence of rigid transformations and dilations that maps F onto G.1 In each of the following problems, two figures are described. Either show that the two figures must be similar using this definition, or give a convincing argument that the two figures need not be similar. (If you claim that two figures are not similar, be sure to provide justification - a picture alone does not count.) (a) Figure Fis the trapezoid in the coordinate plane with vertices at (-6,-4),(-2, -4), (-3,-2), and (-5,-2); figure G is the trapezoid with vertices at (1,2), (5,4). (5,8), and (1,10) (b) Figure F is a parallelogram ABCD with AB CD 10 and BC DA 6, and figure G is a parallelogram PQRS with PQ-RS 15 and QR- SP 9.Explanation / Answer
ANS:-
a) Figure F is the trapezoid in the coordinate plane with vertices at (6,4), (2,4), (3,2),and (5,2); gure G is the trapezoid with vertices at (1,2), (5,4), (5,8), and (1,10). In this case the trapezoids are not similar.
(b) Figure F is a parallelogram ABCD with AB = CD = 10 and BC = DA = 6, and gure G is a parallelogram PQRS with PQ = RS = 15 and QR = SP = 9. Since, the sides of the two parallelogram are in same ratio, therefore, the parallelograms are similar.
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